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IMO Shortlist 2012, Combinatorics 2

Source: IMO Shortlist 2012, Combinatorics 2

July 29, 2013
IMO ShortlistcombinatoricsExtremal combinatoricsDoublecounting

Problem Statement

Let n≥1n \geq 1 be an integer. What is the maximum number of disjoint pairs of elements of the set {1,2,…,n}\{ 1,2,\ldots , n \} such that the sums of the different pairs are different integers not exceeding nn?
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